Blind source separation of pulse oximetry signals

ABSTRACT

A method and apparatus for the application of Blind Source Separation (BSS), specifically independent Component Analysis (ICA) to mixture signals obtained by a pulse oximeter sensor. In pulse oximetry, the signals measured at different wavelengths represent the mixture signals, while the plethysmographic signal, motion artifact, respiratory artifact and instrumental noise represent the source components. The BSS is carried out by a two-step method including an ICA. In the first step, the method uses Principal Component Analysis (PCA) as a preprocessing step, and the Principal Components are then used to derive sat and the Independent Components, where the Independent Components are determined in a second step. In one embodiment, the independent components are obtained by high-order decorrelation of the principal components, achieved by maximizing the sum of the squares of the higher-order cumulants of the plurality of mixture signals.

BACKGROUND OF THE INVENTION

The present invention relates to the processing of signals obtained froma medical diagnostic apparatus such as a pulse oximeter using a blindsource separation technique to separate the obtained data without priorknowledge of its magnitude or frequency into data corresponding to thedesired physiological data and the undesired interference sources.

A typical pulse oximeter measures two physiological parameters, percentoxygen saturation of arterial blood hemoglobin (SpO₂ or sat) and pulserate. Oxygen saturation can be estimated using various techniques. Inone common technique, the photocurrent generated by the photo-detectoris conditioned and processed to determine the ratio of modulation ratios(ratio of ratios) of the red to infrared signals. This modulation ratiohas been observed to correlate well to arterial oxygen saturation. Thepulse oximeters and sensors are empirically calibrated by measuring themodulation ratio over a range of in vivo measured arterial oxygensaturations (SaO₂) on a set of patients, healthy volunteers, or animals.The observed correlation is used in an inverse manner to estimate bloodoxygen saturation (SpO₂) based on the measured value of modulationratios of a patient. The estimation of oxygen saturation usingmodulation ratios is described in U.S. Pat. No. 5,853,364, entitled“METHOD AND APPARATUS FOR ESTIMATING PHYSIOLOGICAL PARAMETERS USINGMODEL-BASED ADAPTIVE FILTERING”, issued Dec. 29, 1998, and U.S. Pat. No.4,911,167, entitled “METHOD AND APPARATUS FOR DETECTING OPTICAL PULSES”,issued Mar. 27, 1990. The relationship between oxygen saturation andmodulation ratio is further described in U.S. Pat. No. 5,645,059,entitled “MEDICAL SENSOR WITH MODULATED ENCODING SCHEME,” issued Jul. 8,1997. Most pulse oximeters extract the plethysmographic signal havingfirst determined saturation or pulse rate, both of which are susceptibleto interference.

A challenge in pulse oximetry is in analyzing the data to obtain areliable measure of a physiologic parameter in the presence of largeinterference sources. Prior art solutions to this challenge haveincluded methods that assess the quality of the measured data anddetermine to display the measured value when it is deemed reliable basedupon a signal quality. Another approach involves a heuristic-basedsignal extraction technology, where the obtained signals are processedbased on a series of guesses of the ratio, and which require thealgorithm to start with a guess of the ratio, which is an unknown. Boththe signal-quality determining and the heuristic signal extractiontechnologies are attempts at separating out a reliable signal from anunreliable one, one method being a phenomenological one and the otherbeing a heuristic one.

On the other hand, a problem encountered in such disciplines asstatistics, data analysis, signal processing, and neural networkresearch, is finding a suitable representation of multivariate data. Onesuch suite of methods is generally known as Independent ComponentAnalysis (ICA), which is an approach to the problem of Blind SourceSeparation (BSS).

In general terms, the goal of blind source separation in signalprocessing is to recover independent source signals after they arelinearly mixed by an unknown medium, and recorded or measured at Nsensors. The blind source separation has been studied by researchers inspeech processing or voice processing; antenna array processing; neuralnetwork and statistical signal processing communities (e.g. P. Comon,“Independent Component Analysis, a New Concept?”, Signal Processing,vol. 36. no. 3, (April 1994), pp. 287-314, “Comon”) and applied withrelative degrees of success to electroencephalogram data and functionalMRI imaging.

Comon defined the concept of independent component analysis asmaximizing the degree of statistical independence among outputs using“contrast” functions of higher-order cumulants. Higher-order statisticsrefer to the expectations of products of three or more signals (e.g.3^(rd)-order or 4^(th)-order moments), and cumulants are functions ofthe moments which are useful in relating the statistics to those of theGaussian distribution. The 3^(rd)-order cumulant of a distribution iscalled a skew, and the 4^(th)-order cumulant is the kurtosis. A contrastfunction is any non-linear function which is invariant to permutationand scaling matrices, and attains its minimum value in correspondence ofthe mutual independence among the output components. In contrast withdecorrelation techniques such as Principal Component Analysis (PCA),which ensures that output pairs are uncorrelated, ICA imposes the muchstronger criterion that the multivariate probability density function ofoutput variables factorizes. Finding such a factorization requires thatthe mutual information between all variable pairs go to zero. Mutualinformation depends on all higher-order statistics of the outputvariables while decorrelation normally only takes account of 2nd-orderstatistics.

While the general use of ICA as a means of blindly separatingindependent signal sources is known, the method poses unique challengesto its implementation in pulse oximetry. For instance, the mixturesignals may not be exactly a linear combination of the pulse signal andsources of interference. Also, most ICA techniques are based onfourth-order cumulants, as the signals and noise commonly encountered incommunications have zero third-order cumulant (skew), and cumulants ofhigher than fourth order are difficult to estimate accurately.

Several ICA methods are known for separating unknown source signals fromsets of mixture signals, where the mixture signals are a linearcombination of the source signals. As used in pulse oximetry, themixture signals refer to signals measured at multiple wavelengths.Source components refer to the desired physiologic data includingsignals corresponding to the plethysmographic signal obtained atmultiple wavelengths in addition to undesired interference data, whichmay be caused by motion, light interference, respiratory artifacts, andother known sources of errors in pulse oximetry.

There is therefore a need to apply blind source separation techniques tothe field of pulse oximetry to be able to deterministically separate asource signal from various interference sources.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed towards a method and apparatus for theapplication of Blind Source Separation (BSS), specifically IndependentComponent Analysis (ICA) to pulse oximetry. ICA refers to any one ofseveral methods for separating unknown source signals from a set of“mixture” signals, which are linear combinations of the source signals.These methods may use estimates of the second- and higher-order jointstatistics of the mixture signals and separate the sources by seeking tominimize the mutual information of the outputs of separation. In pulseoximetry, the signals measured at different wavelengths represent themixture signals, while the plethysmographic signal, motion artifact,respiratory artifact and instrumental noise represent the sourcecomponents.

In one embodiment the BSS is carried out by a two-step method includingPCA and a higher-order decorrelation. In the first step, the method usesPCA as a preprocessing step, and in a second step, the principalcomponents are then used to derive the independent components and thedesired physiological parameters. The PCA is performed to transform thedata to have zero second-order correlation before higher-orderdecorrelation.

In one aspect of the method of the present invention, data correspondingto a plurality of signals measured at a plurality of wavelengths arefirst obtained. Next, the data are processed to obtain a plurality ofprincipal components, where in one embodiment the principal componentsare obtained by decorrelating the data (to minimize thecross-correlation between the signals from different wavelengths), andnormalizing the decorrelated data. Next, the principal components areprocessed to obtain a plurality of independent components, wherein amatrix of the plurality of signals corresponds with a matrix product ofa matrix of the plurality of independent components and a matrix ofmixing coefficients. In one embodiment, the independent components areobtained by higher-order decorrelation of the principal components, andwhere the higher-order decorrelation of the principal components isachieved by minimizing a function of the higher-order cross-correlationof the data or equivalently by maximizing a function of the higher-ordercumulants of the plurality of mixture signals. Since the skew of thetime-derivative of the pulse signal is generally much greater inmagnitude than that of interference, performance of the ICA may beenhanced by using a “contrast” function that was derived from thethird-order cumulants of the derivatives of the signals.

In an aspect of the method of the present invention directed towards apulse oximeter measuring signals at multiple wavelengths, a firstindependent component corresponds with a plethysmographic signal, asecond independent component corresponds with the interference sources,and sat may be determined from a ratio of mixing coefficients from themixing matrix. In pulse oximetry, the technique provides the advantageof extracting the plethysmographic signal in the presence of largemotion interference and especially without requiring prior knowledge ofsaturation or pulse rate.

For a further understanding of the nature and advantages of theinvention, reference should be made to the following description takenin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an exemplary pulse oximeter.

FIG. 2 is a flow chart of an embodiment of the method of the presentinvention.

FIG. 3 is a graph showing a typical pulse oximetry signals at twowavelengths.

FIG. 4 is a graph showing the typical pulse oximetry signals at twowavelengths after PCA processing.

FIG. 5 is a graph showing a typical pulse oximetry signals at twowavelengths after ICA processing.

FIG. 6 is a graph of signals of FIG. 3 plotted against one another.

FIG. 7 is a graph of the principal components of FIG. 3 plotted againstone another.

FIG. 8 is a graph of the independent components of FIG. 3 plottedagainst one another.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed towards the application of BlindSource Separation (BSS), specifically Independent Component Analysis(ICA) to pulse oximetry. ICA refers to any one of several methods forseparating unknown source signals from a set of “mixture” signals, whichare linear combinations of the source signals. The ICA method asembodied by the present invention, uses estimates of the second- andhigher-order joint statistics of the mixture signals and separates thesources by seeking to minimize the mutual information of the outputs ofseparation. In pulse oximetry, the signals measured at differentwavelengths represent the mixture signals, while the plethysmographicsignal, motion artifact, respiratory artifact and instrumental andenvironmental noise represent the source components.

In one embodiment, the BSS is carried out by a two-step method includingan ICA. In the first step, the method uses Principal Component Analysis(PCA) as a preprocessing step, and the Principal Components are thenused to derive sat and Independent Components, where the IndependentComponents are determined in the second step. Before describing the BSSmethods of the present invention an example of a pulse oximeter, whichmay be configured to practice the method of the present invention isdescribed below.

FIG. 1 is a block diagram of one embodiment of a pulse oximeterimplementing the present invention. Light from light source 110 passesinto patient tissue 112, and is scattered and detected by photodetector114. A sensor 100 containing the light source and photodetector may alsocontain an encoder 116 which provides signals indicative of thewavelength of light source 110 to allow the oximeter to selectappropriate calibration coefficients for calculating oxygen saturation.Encoder 116 may, for instance, be a resistor.

Sensor 100 is connected to a pulse oximeter 120. The oximeter includes amicroprocessor 122 connected to an internal bus 124. Also connected tothe bus is a RAM memory 126 and a display 128. A time processing unit(TPU) 130 provides timing control signals to light drive circuitry 132which controls when light source 110 is illuminated, and if multiplelight sources are used, the multiplexed timing for the different lightsources. TPU 130 also controls the gating-in of signals fromphotodetector 114 through an amplifier 133 and a switching circuit 134.These signals are sampled at the proper time, depending upon which ofmultiple light sources is illuminated, if multiple light sources areused. The received signal is passed through an amplifier 136, a low passfilter 138, and an analog-to-digital converter 140. The digital data isthen stored in a queued serial module (QSM) 142, for later downloadingto RAM 126 as QSM 142 fills up. In one embodiment, there may be multipleparallel paths of separate amplifier filter and A/D converters formultiple light wavelengths or spectrums received.

Based on the value of the received signals corresponding to the lightreceived by photodetector 114, microprocessor 122 will calculate theoxygen saturation using various algorithms. These algorithms requirecoefficients, which may be empirically determined, corresponding to, forexample, the wavelengths of light used. These are stored in a ROM 146.The particular set of coefficients chosen for any pair of wavelengthspectrums is determined by the value indicated by encoder 116corresponding to a particular light source in a particular sensor 100.In one embodiment, multiple resistor values may be assigned to selectdifferent sets of coefficients. In another embodiment, the sameresistors are used to select from among the coefficients appropriate foran infrared source paired with either a near red source or far redsource. The selection between whether the near red or far red set willbe chosen can be selected with a control input from control inputs 154.Control inputs 154 may be, for instance, a switch on the pulse oximeter,a keyboard, or a port providing instructions from a remote hostcomputer. Furthermore any number of methods or algorithms may be used todetermine a patient's pulse rate, oxygen saturation or any other desiredphysiological parameter. One such method, namely Blind SourceSeparation, is described below.

Blind Source Separation refers to the separation of signals given onlylinear combinations of those signals, such that:

x(t)=A s(t)

where x(t) is a matrix of a set of observed signals (mixed signals),x₁(t) . . . x_(n)(t),

A is an unknown mixing matrix,

and s(t) is a set of source signals s₁(t) . . . s_(m)(t),

assumed to be statistically independent, i.e.${p(s)} = {{p\left( {s_{1},\ldots \quad,s_{m}} \right)} = {\prod\limits_{i = 1}^{m}\quad {p_{i}\left( s_{i} \right)}}}$

where p(s) is the probability distribution function of s.

As described above, in pulse oximetry, the mixture signals correspondwith signals obtained by a pulse oximeter sensor, which include both thedesired signal and the undesired noise components. In one embodiment ofthe method of the present invention, the mixture signals are firstpreprocessed using PCA to transform the mixture signal to principalcomponents. To more fully separate the signal and the noise, the dataare further processed: in mathematical terms, the data are rotated. Inother words, the ICA processing includes a combination of PCA androtation.

A criterion for determining the degree of signal-noise separation isstatistical independence, as described above. However, since theprobability distributions are not known, the challenge of an ICAalgorithm becomes the measurement of statistical independence. A measureof statistical independence is the degree of mutual information, suchthat by minimizing the degree of mutual information between sets ofdata, independent components can be determined. Algorithms determiningthe mutual information are generally too complicated for a directsolution of its (i.e. mutual information) minimum, and thus they lendthemselves best to iterative methods. For example, one possible approachwould be to search for coefficients of the mixing matrix A that wouldlead to statistical independence (by minimizing the data set's mutualinformation). One could heuristically sweep through a large range ofangles about which to rotate the principal components, which would yieldan independent set of data, but this approach would be excessivelytime-consuming.

Thus the inventor of the present invention proposes separating the databy performing higher-order decorrelation of the data, or by removing thehigher-order correlation of the data obtained from the mixture signals.Thus, the BSS-based method of the present invention: (1) uses PCA tofind uncorrelated components, and (2) separates the data by removinghigher-order correlation to find the independent componentscorresponding with the desired signal source(s) and the undesired noisesources. And as used herein, higher-order correlations are higher thansecond-order correlations, such as third-order and fourth-ordercross-correlations. In one embodiment, independence is approximated byminimizing the sum of the squares of the third-order correlationsr_(xxy) and r_(xyy), e.g.,$r_{XXY} = {{\sum\limits_{i}{x_{i}^{2}y_{i}\quad {and}\quad r_{XYY}}} = {\sum\limits_{i}{x_{i}y_{i}^{2}}}}$

[where x and y have zero mean]

Alternately, independence is approximated by minimizing the sum of thesquares of the fourth-order cross-cumulants.

In certain embodiments of the present invention, separation is achievedby maximizing the sum of the squares of the higher-order cumulants,which is equivalent to minimizing the sum of the squares of thehigher-order cross-cumulants. In these and other embodiments, thesecond-order decorrelation and higher-order decorrelation may beeffected simultaneously through an iterative, adaptive process.

The advantage of achieving separation by higher-order decorrelation isthat it enables direct formulas and simple algorithms for the separationof data into its independent components.

FIG. 2 is a flow chart 200 of an embodiment the method of the presentinvention as applied to signals obtained by a pulse oximeter sensor.First, (step 210) a plurality of signals measured at various wavelengthsare obtained by a pulse oximeter sensor. In a typical pulse oximeter,emitting optical energy at two wavelengths, the photocurrent generatedby the photo-detector is conditioned and processed to determine themodulation ratios of the red and infrared signals. The example of atwo-wavelength pulse oximeter is for illustration purposes only, and isnot meant to limit the scope of the present invention. The detectedphotocurrents include the mixture signals, where the mixture signalsinclude the plethysmographic signal, motion artifact, respiratoryartifact and instrument noise. An example plot of the measuredphotocurrent is shown on FIG. 3. FIG. 3 shows a plot 300 of thephotocurrent vs. time for measurements obtained at 595 nm (310) and at665 nm (320). As can be seen from this figure (FIG. 3), both signals(310 and 320) show a low amplitude section and a high amplitude section,where the high amplitude section corresponds to the signals measuredwhile the sensor is moving.

Next, (step 220) the mixture signals are processed using PCA analysis toobtain two principal components. Here, the PCA processing results in thedetermination of two principal components, since the original mixturesignals were obtained at two different wavelengths. Embodiments of thepresent invention are not limited to two mixture signals or twoprincipal components. The embodiments of the present invention aredirected to the decomposition of a matrix of a set of observed signals(mixed signals) into a set of source signals and a mixing matrix, as setforth above. However, describing more than two dimensions andvisualizing more dimensions is at best difficult to visualize, hence thedescription provided herein is kept to a two-dimensional one. In oneembodiment, the Singular Value Decomposition algorithm is used to obtainthe principal components. In one alternate embodiment, the data aremultiplied by the inverse of the square root of the covariance matrix.In another embodiment directed to a two wavelengths approach, for eachpossible pair of wavelengths, the data are rotated by the angle of thebest linear fit between those two signals. FIG. 4 shows a plot 400 ofthe two principal components. As can be seen from this figure (FIG. 4),the first principal component 410 corresponds more with the noise due tothe subject's motion, since it has a low amplitude portion, which isfollowed by a high amplitude portion. FIG. 4 also shows that the secondprincipal component 420 corresponds less with the noise due to thesubject movement, since it does not show a distinct high amplitudeportion.

Furthermore, a comparison of FIGS. 6 and 7 shows that while the originalmixture signals are not decorrelated, the principal components aredecorrelated. FIG. 6 shows a graph of the photocurrent at 655 nm vs. thephotocurrent at 595 nm. As can be seen from this figure (FIG. 6), thereis a wealth of mutual information between the two photocurrents, sincethe data from the two photocurrents appear to be aligned along thepositively sloping diagonal line A—A. FIG. 7 shows a plot of principalcomponent 2 vs. principal component 1. A review of this figure (FIG. 7)shows that the principal components are decorrelated, since there is nosignificant linear fit to the data in these coordinates.

In an alternate embodiment, before the processing according to step 220,the time derivatives of the signals are obtained. For pulse oximetry,the third-order correlations of the pulse signals are often enhanced bytaking the time derivative of the signals before performing PCA/ICAanalyses.

Having decorrelated the data, the principal components are furtherprocessed by ICA processing to determine the independent componentsdescribing the photocurrent data (step 230). As described above, theprincipal components are processed to obtain a plurality of independentcomponents, wherein a matrix of the plurality of signals correspondswith a matrix product of a matrix of the plurality of independentcomponents and a matrix of mixing coefficients. In one embodiment, theindependent components are determined by decorrelating the data bymaximizing the sum of squares of the data set's higher-order cumulants.Since the skew of the time-derivative of the pulse signal is generallymuch greater in magnitude than that of interference, the ICA performanceis enhanced by using a “contrast” function that was derived from thethird-order cumulants of the derivatives of the signals. As statedabove, a contrast function is any non-linear function which is invariantto permutation and scaling matrices, and attains its minimum value incorrespondence of the mutual independence among the output components.In an alternate embodiment, the independent components are determined byminimizing the estimated mutual information. FIG. 5 shows a plot 500 ofthe two independent components. As can be seen from this figure (FIG.5), a first independent component 510 corresponds more with the noisedue to the subject's motion, since it has a low amplitude portion, whichis followed by a high amplitude portion. FIG. 5 also shows that a secondprincipal component 520 apparently corresponds to a pulse component.Furthermore, FIG. 8 shows a plot of independent component 2 vs.independent component 1. As can be seen from this figure (FIG. 8), theplot of independent component 2 vs. independent component 1 lies alongthe horizontal line at (independent component=0) B—B, showing that thedata sets have a minimal amount of mutual information, and thus can beapproximated as independent data sets.

The decomposed data set of two independent components is furtherprocessed as follows. In one embodiment, sat is obtained from a ratio ofmixing coefficients (step 240). In an alternate embodiment, one of theindependent components is further processed to obtain theplethysmographic signal (step 250), and the other independent signal isrecognized as a measure of the interference signal (step 260).

Alternately, instead of, or in addition to taking signals that aremeasured at different wavelengths (step 210), signals are also obtainedthat are additions of signals from different times, thus an alternateembodiment of the present invention starts by processing signalsobtained from mixing signals in time.

In pulse oximetry, embodiments of the present invention have theadvantage of extracting the plethysmographic signal in the presence oflarge motion interference and especially without requiring priorknowledge of saturation or pulse rate. Additionally, the present methodis extendible to measurement of other physiological variables, such aspulse rate, blood pressure, temperature, or any other physiologicalvariable measurable by non-invasive measurement of photocurrent providedan optical-based sensor.

Accordingly, as will be understood by those of skill in the art, thepresent invention which is related to blind source separation of pulseoximetry signals, may be embodied in other specific forms withoutdeparting from the essential characteristics thereof. Accordingly, theforegoing disclosure is intended to be illustrative, but not limiting,of the scope of the invention, which is set forth in the followingclaims.

What is claimed is:
 1. A method for measuring a physiological parameter,comprising: measuring a plurality of signals, wherein each of saidsignals comprises a source component corresponding to said physiologicalparameter and an interference component; processing said plurality ofsignals to obtain a plurality of principal components; processing saidplurality of principal components to obtain a plurality of independentcomponents, wherein a matrix of said plurality of signals corresponds toa matrix product of a matrix of said plurality of independent componentsand a matrix of mixing coefficients; and extracting a first measure ofsaid physiological parameter corresponding to said source component fromone of said plurality of independent components, wherein said pluralityof signals corresponds to sensed optical energies from a plurality ofwavelengths.
 2. The method of claim 1 wherein said physiologicalparameter is a function of an oxygen saturation.
 3. The method of claim1 wherein said processing said plurality of signals further comprisesobtaining a time derivative of the sensed optical energies from aplurality of wavelengths.
 4. The method of claim 1 wherein saidinterference component comprises signal components caused by motion,respiratory artifact, ambient light, optical scattering and otherinterference between a tissue location being sensed and a sensor.
 5. Themethod of claim 1 wherein said processing said plurality of signalsfurther comprises decorrelating said plurality of signals by minimizinga cross-correlation of said plurality of signals, to obtain a pluralityof decorrelated signals; and normalizing said plurality of decorrelatedsignals to obtain the plurality of principal components.
 6. The methodof claim 1 wherein said processing said plurality of signals comprisesdecorrelating said plurality of signals by singular-value decompositionof said plurality of signals, to obtain the plurality of principalcomponents.
 7. The method of claim 1 wherein said processing saidplurality of signals comprises decorrelating said plurality of signalsby multiplying said plurality of signals the inverse square root of thecovariance matrix of said plurality of signals to obtain the pluralityof principal components.
 8. The method of claim 1 wherein saidprocessing of said plurality of principal components compriseshigher-order decorrelation of said plurality of principal components.9.The method of claim 1 wherein said processing said plurality ofprincipal components comprises maximizing a function of the higher-ordercumulants of a mixture of said plurality of signals, thus separatingsaid source component from said interference component.
 10. The methodof claim 9 wherein said higher-order cumulant is cumulant having ordergreater than two.
 11. The method of claim 9 wherein said higher-ordercumulant is a third-order cumulant of said plurality of signals.
 12. Themethod of claim 9 wherein said higher-order cumulant is a fourth-ordercumulant of said plurality of signals.
 13. The method of claim 1 furthercomprising obtaining a ratio of mixing coefficients from said matrix ofmixing coefficients, wherein said ratio corresponds to a ratio ofmodulation ratios of red to infrared signals, wherein said plurality ofsignals comprise modulated optical signals in the red and infraredranges.
 14. The method of claim 13 further comprising extracting asecond measure of said physiological parameter from said ratio, whereinsaid second measure of said physiological parameter corresponds to anoxygen saturation.
 15. The method of claim 1 further comprisingextracting said interference component from another one of saidplurality of independent components.
 16. A method for measuring aphysiological parameter, comprising: measuring a plurality of signals,wherein each of said signals comprises a source component correspondingto said physiological parameter and an interference component;processing said plurality of signals to obtain a plurality of principalcomponents; processing said plurality of principal components to obtaina plurality of independent components, wherein a matrix of saidplurality of signals corresponds to a matrix product of a matrix of saidplurality of independent components and a matrix of mixing coefficients;and extracting a first measure of said physiological parametercorresponding to said source component from one of said plurality ofindependent components, wherein said physiological parameter is afunction of a pulse rate.
 17. A method for measuring a physiologicalparameter, comprising: measuring a plurality of signals, wherein each ofsaid signals comprises a source component corresponding to saidphysiological parameter and an interference component; processing saidplurality of signals to obtain a plurality of principal components;processing said plurality of principal components to obtain a pluralityof independent components, wherein a matrix of said plurality of signalscorresponds to a matrix product of a matrix of said plurality ofindependent components and a matrix of mixing coefficients; andextracting a first measure of said physiological parameter correspondingto said source component from one of said plurality of independentcomponents, wherein said plurality of signals corresponds to sensedoptical energies from a plurality of wavelengths from different times.18. A method for measuring a physiological parameter, comprising:measuring a plurality of signals, wherein each of said signals comprisesa source component corresponding to said physiological parameter and aninterference component; processing said plurality of signals to obtain aplurality of principal components; processing said plurality ofprincipal components to obtain a plurality of independent components,wherein a matrix of said plurality of signals corresponds to a matrixproduct of a matrix of said plurality of independent components and amatrix of mixing coefficients; and extracting a first measure of saidphysiological parameter corresponding to said source component from oneof said plurality of independent components, wherein said first measureof a physiological parameter corresponds to a pulse rate.
 19. A pulseoximeter, comprising: a sensor configured for measuring a plurality ofsignals, wherein each of said signals comprises a source componentcorresponding to said physiological parameter and an interferencecomponent; a computer useable medium having computer readable codeembodied therein for measuring a physiological parameter, said computerreadable code configured to execute functions comprising: processingsaid plurality of signals to obtain a plurality of principal components;processing said plurality of principle components to obtain a pluralityof independent components, wherein a matrix of said plurality of signalscorresponds to a matrix product of a matrix of said plurality ofindependent components and a matrix of mixing coefficients; andextracting a first measure of said physiological parameter correspondingto said source component from one of said plurality of independentcomponents, wherein said physiological parameter is a pulse rate.
 20. Apulse oximeter, comprising: a sensor configured for measuring aplurality of signals, wherein each of said signals comprises a sourcecomponent corresponding to said physiological parameter and aninterference component; a computer useable medium having computerreadable code embodied therein for measuring a physiological parameter,said computer readable code configured to execute functions comprising:processing said plurality of signals to obtain a plurality of principalcomponents; processing said plurality of principle components to obtaina plurality of independent components, wherein a matrix of saidplurality of signals corresponds to a matrix product of a matrix of saidplurality of independent components and a matrix of mixing coefficients;and extracting a first measure of said physiological parametercorresponding to said source component from one of said plurality ofindependent components, wherein said plurality of signals corresponds tosensed optical energies from a plurality of wavelengths.
 21. The pulseoximeter of claim 20 wherein said physiological parameter is an oxygensaturation.
 22. The pulse oximeter of claim 20 wherein said plurality ofsignals corresponds to the time derivative of the sensed opticalenergies from a plurality of wavelengths.
 23. The pulse oximeter ofclaim 20 wherein said interference component comprises signal componentscaused by motion, respiratory artifact, ambient light, opticalscattering and other interference between a tissue location being senseand a sensor.
 24. The pulse oximeter of claim 20 wherein said processingsaid plurality of signals comprises decorrelating said plurality ofsignals by minimizing a cross-correlation of said plurality of signals,to obtain a plurality of decorrelated signals; and normalizing saidplurality of decorrelated signals to obtain the plurality of principalcomponents.
 25. The pulse oximeter of claim 20 wherein said processingsaid plurality of signals comprises decorrelating said plurality ofsignals by singular-value decomposition of said plurality of signals, toobtain the plurality of principal components.
 26. The pulse oximeter ofclaim 20 wherein said processing said plurality of signals comprisesdecorrelating said plurality of signals by multiplying said plurality ofsignals by the inverse square root of the covariance matrix of saidplurality of signals to obtain the plurality of principal components.27. The pulse oximeter of claim 20 wherein said processing of saidplurality of principal components comprises higher-order decorrelationof said plurality of principal components.
 28. The pulse oximeter ofclaim 20 wherein said processing said plurality of principal componentscomprises maximizing a function of the higher-order cumulants of amixture of said plurality of signals, thus separating said sourcecomponent from said interference component.
 29. The pulse oximeter ofclaim 28, wherein said higher-order cumulant is cumulant having ordergreater than two.
 30. The pulse oximeter of claim 28, wherein saidhigher-order order cumulant is a third-order cumulant of said pluralityof signals.
 31. The pulse oximeter of claim 28 wherein said higher-orderorder cumulant is a fourth-order cumulant of said plurality of signals.32. The pulse oximeter of claim 20 wherein said processing saidplurality of principal components comprises successive transformationsto simultaneously minimize second- and higher-order correlations amongthe outputs of the transformations.
 33. The pulse oximeter of claim 20wherein said processing said plurality of principal components comprisessuccessive rotations to minimize estimated mutual information amongoutputs of the invention.
 34. The pulse oximeter of claim 20 furthercomprising obtaining a ratio of mixing coefficients from said matrix ofmixing coefficients, wherein said ratio corresponds to a ratio ofmodulation ratios of red to infrared signals.
 35. The pulse oximeter ofclaim 34 further comprising extracting a second measure of saidphysiological parameter from said ratio, wherein said second measure ofsaid physiological parameter corresponds to an oxygen saturation. 36.The pulse oximeter of claim 20 wherein said first measure of aphysiological parameter corresponds a pulse rate.
 37. The pulse oximeterof claim 20 further comprising extracting said interference componentfrom another one of said plurality of independent components.
 38. Apulse oximeter, comprising: a sensor configured for measuring aplurality of signals, wherein each of said signals comprises a sourcecomponent corresponding to said physiological parameter and aninterference component; a computer useable medium having computerreadable code embodied therein for measuring a physiological parameter,said computer readable code configured to execute functions comprising:processing said plurality of signals to obtain a plurality of principalcomponents; processing said plurality of principle components to obtaina plurality of independent components, wherein a matrix of saidplurality of signals corresponds to a matrix product of a matrix of saidplurality of independent components and a matrix of mixing coefficients;and extracting a first measure of said physiological parametercorresponding to said source component from one of said plurality ofindependent components, wherein said plurality of signals corresponds tosensed optical energies from a plurality of wavelengths from differenttimes.